Question: What is the largest prime factor of 999?
Answer: First, divide out 9 to obtain $999=9\cdot111$.  Since $1+1+1=3$, 111 is divisible by 3.  Dividing, we find $111=3\cdot 37$.  Therefore, $999=3^2\cdot 3\cdot 37=3^3\cdot 37$ and the largest prime factor of 999 is $\boxed{37}$.